3.6 Graphs of Functions

Before you get started, take this readiness quiz.

Evaluate: ⓐ $2^{3}$ ⓑ $3^{2} .$
If you missed this problem, review the reference.

Evaluate: ⓐ $\left|7\right|$ ⓑ $\left|−3\right| .$
If you missed this problem, review the reference.

Evaluate: ⓐ $\sqrt{4}$ ⓑ $\sqrt{16} .$
If you missed this problem, review the reference.

Determine which ordered pairs are solutions to the given equations.

$5 x + y = 10 ;$
ⓐ $\left(5 , 1\right)$
ⓑ $\left(2 , 0\right)$
ⓒ $\left(4 , −10\right)$

Find the intercepts of each equation.

$x + 2 y = 6$

Find the intercepts of each equation.

$y = \frac{3}{4} x - 12$

Find the slope of each line.

$x = 5$

Find the slope of each line.

$y = −1$

Use the slope formula to find the slope of the line between each pair of points.

$\left(3,5\right) , \left(4 , −1\right)$

Use the slope formula to find the slope of the line between each pair of points.

$\left(2 , 1\right) , \left(4 , 6\right)$

Identify the slope and y-intercept of each line.

$y = \frac{5}{3} x - 6$

Identify the slope and y-intercept of each line.

$4 x - 5 y = 8$

Determine the most convenient method to graph each line.

$y = −3$

Determine the most convenient method to graph each line.

$x - y = 2$

Determine the most convenient method to graph each line.

$y = \frac{3}{4} x - 1$

Use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

$y = 5 x - 1 ; 10 x + 2 y = 0$

Use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

$2 x - y = 8 ; x - 2 y = 4$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $−5$ and $y$-intercept $\left(0 , −3\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $−2$ and $y$-intercept $\left(0 , 0\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = \frac{3}{5} ,$ point $\left(10 , 6\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = −2 ,$ point $\left(−1 , −3\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(7 , 1\right)$ and $\left(5 , 0\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(5 , 2\right)$ and $\left(−1 , 2\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $2 x + 5 y = −10 ,$ point $\left(10 , 4\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $y = −5 ,$ point $\left(−4 , 3\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $2 x - 3 y = 9 ,$ point $\left(−4 , 0\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $x = −5$ point $\left(2 , 1\right)$

Determine whether each ordered pair is a solution to the given inequality.

Determine whether each ordered pair is a solution to the inequality $x + y > 4 :$

ⓐ $\left(6 , 1\right)$ ⓑ $\left(−3 , 6\right)$ ⓒ $\left(3 , 2\right)$ ⓓ $\left(−5 , 10\right)$ ⓔ $\left(0 , 0\right)$

For each relation, ⓐ find the domain of the relation ⓑ find the range of the relation.

$\left\{\right. \left(−3 , 7\right) , \left(−2 , 3\right) , \left(−1 , 9\right) ,$
$\left(0 , −3\right) , \left(−1 , 8\right) \left.\right\}$

Use the set of ordered pairs to ⓐ determine whether the relation is a function ⓑ find the domain of the relation ⓒ find the range of the relation.

$\left\{\right. \left(−3 , 27\right) , \left(−2 , 8\right) , \left(−1 , 1\right) ,$
$\left(0 , 0\right) , \left(1 , 1\right) , \left(2 , 8\right) , \left(3 , 27\right) \left.\right\}$

Determine whether each equation is a function.

$y = x^{2}$

Determine whether each equation is a function.

$y = x^{3}$

ⓐ $f \left(−2\right)$ ⓑ $f \left(3\right)$ ⓒ $f \left(a\right) .$

$f \left(x\right) = 3 x - 4$

ⓐ $f \left(−2\right)$ ⓑ $f \left(3\right)$ ⓒ $f \left(a\right) .$

$f \left(x\right) = x^{2} - 5 x + 6$

Evaluate the function.

$g \left(x\right) = 3 x^{2} - 5 x ;$ $g \left(2\right)$

Evaluate the function.

$h \left(t\right) = 4 \left|t - 1\right| + 2 ;$ $h \left(−3\right)$

Find the equation of each line. Write the equation in slope-intercept form.

$m = 2 ,$ point $\left(−3 , −1\right)$

Find the equation of each line. Write the equation in slope-intercept form.

perpendicular to the line $y = \frac{5}{4} x + 2 ,$ containing the point $\left(−10 , 3\right)$

Graph each linear inequality.

Use the set of ordered pairs to ⓐ determine whether the relation is a function, ⓑ find the domain of the relation, and ⓒ find the range of the relation.

$\left\{\right. \left(−3 , 27\right) , \left(−2 , 8\right) , \left(−1 , 1\right) , \left(0 , 0\right) ,$
$\left(1 , 1\right) , \left(2 , 8\right) , \left(3 , 27\right) \left.\right\}$

Graph each linear inequality.

For $h \left(y\right) = 3 \left|y - 1\right| - 3 ,$ evaluate $h \left(−4\right) .$